In general if you want to use the bike for proper off road then look for Shimano LX or SRAM X7 or better components.

Check that the gear shifting is smooth with no chain jump when riding in a particular gear.

If the bike has disc brakes cycle the brake lever a few times and make sure you can feel a positive contact point at the lever. The wheels should turn freely without the pads rubbing on the disc. It is reasonably normal to have to readjust this if you remove a wheel.

Check the suspension that it cycles well through its travel, and that the rebound works smoothly.

Check the suspension stanchions that there is no damage and that it is smooth to run in and out of the dust boots.

Check that the wheels run reasonably true. Differentiate between the wheel running true and the tyre running true. A minor error in seating of the tyre can look like the wheel is bent when it is actually only the tyre.

Check for play in the rear triangle of a full suspension bike.

Check for play in bottom bracket and the headset.

In general providing the frame is sound most other things can be replaced. Some at larger cost then others. But if you are using a bike offroad then you need to count with a little maintenance and occasional replacement parts.

If you are interested I will have a full suspension Trek Fuel EX8 for sale in the next few weeks. The bike is two years old and has been regularly serviced and maintained. The only wear that I have on it at the moment is the chain and I am waiting for a new one to come so that it runs the way it did the day I bought it before I sell it.